How do you find the inverse of f(x)=3x-5?

2 Answers
Apr 17, 2018

f(x)^-1 =1/3x+5/3

Explanation:

f(x)=3x-5
The inverse of a function completely swaps the x and y values. One way to find the inverse of a function is to switch the "x" and "y" in a equation
y=3x-5 turns into x=3y-5
Then solve the equation for y
x=3y-5
x+5=3y
1/3x+5/3=y
f(x)^-1 =1/3x+5/3

Apr 17, 2018

f(x)=3x-5

y=3x-5

x=3y-5

add three to both sides

3y=x+5

divide by three on both sides

f^-1(x)=5/3 + x/3

f^-1(x)=x+5 /3